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(Top)
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1
Iterative algorithm
| https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#Iterative_algorithm |
|
1.1
Cache behavior
| https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#Cache_behavior |
|
2
Divide-and-conquer algorithm
| https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#Divide-and-conquer_algorithm |
|
2.1
Non-square matrices
| https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#Non-square_matrices |
|
2.2
Cache behavior
| https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#Cache_behavior_2 |
|
3
Sub-cubic algorithms
| https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#Sub-cubic_algorithms |
|
3.1
AlphaTensor
| https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#AlphaTensor |
|
4
Parallel and distributed algorithms
| https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#Parallel_and_distributed_algorithms |
|
4.1
Shared-memory parallelism
| https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#Shared-memory_parallelism |
|
4.2
Communication-avoiding and distributed algorithms
| https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#Communication-avoiding_and_distributed_algorithms |
|
4.3
Algorithms for meshes
| https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#Algorithms_for_meshes |
|
5
See also
| https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#See_also |
|
6
References
| https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#References |
|
7
Further reading
| https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#Further_reading |
| Català | https://ca.wikipedia.org/wiki/Algorisme_de_multiplicaci%C3%B3_de_matrius |
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| Српски / srpski | https://sr.wikipedia.org/wiki/Algoritam_mno%C5%BEenja_matrica |
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| Wikidata item | https://www.wikidata.org/wiki/Special:EntityPage/Q17082383 |
| matrix multiplication | https://en.wikipedia.org/wiki/Matrix_multiplication |
| numerical algorithms | https://en.wikipedia.org/wiki/Numerical_algorithm |
| scientific computing | https://en.wikipedia.org/wiki/Scientific_computing |
| pattern recognition | https://en.wikipedia.org/wiki/Pattern_recognition |
| graph | https://en.wikipedia.org/wiki/Graph_(graph_theory) |
| [1] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-skiena-1 |
| parallel | https://en.wikipedia.org/wiki/Parallel_computing |
| distributed | https://en.wikipedia.org/wiki/Distributed_computing |
| takes time | https://en.wikipedia.org/wiki/Analysis_of_algorithms |
| field | https://en.wikipedia.org/wiki/Field_(mathematics) |
| big O notation | https://en.wikipedia.org/wiki/Big_O_notation |
| asymptotic bounds | https://en.wikipedia.org/wiki/Asymptotic_bound |
| Strassen's algorithm | https://en.wikipedia.org/wiki/Strassen_algorithm |
| computational complexity of matrix multiplication | https://en.wikipedia.org/wiki/Computational_complexity_of_matrix_multiplication |
| [update] | https://en.wikipedia.org/w/index.php?title=Matrix_multiplication_algorithm&action=edit |
| asymptotic complexity | https://en.wikipedia.org/wiki/Time_complexity |
| Williams | https://en.wikipedia.org/wiki/Virginia_Vassilevska_Williams |
| [2] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-alman2025-2 |
| galactic algorithm | https://en.wikipedia.org/wiki/Galactic_algorithm |
| edit | https://en.wikipedia.org/w/index.php?title=Matrix_multiplication_algorithm&action=edit§ion=1 |
| definition of matrix multiplication | https://en.wikipedia.org/wiki/Matrix_multiplication#Definition |
| simple algorithm | https://en.wikipedia.org/wiki/SIMPLE_algorithm |
| time | https://en.wikipedia.org/wiki/Time_complexity |
| asymptotic notation | https://en.wikipedia.org/wiki/Asymptotic_notation |
| [1] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-skiena-1 |
| algorithm analysis | https://en.wikipedia.org/wiki/Analysis_of_algorithms |
| [3] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-clrs-3 |
| edit | https://en.wikipedia.org/w/index.php?title=Matrix_multiplication_algorithm&action=edit§ion=2 |
| https://en.wikipedia.org/wiki/File:Row_and_column_major_order.svg |
| row- and column-major order | https://en.wikipedia.org/wiki/Row-_and_column-major_order |
| memory access patterns | https://en.wikipedia.org/wiki/Locality_of_reference |
| cache | https://en.wikipedia.org/wiki/CPU_cache |
| [1] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-skiena-1 |
| row-major order, column-major order | https://en.wikipedia.org/wiki/Row-_and_column-major_order |
| fully associative cache | https://en.wikipedia.org/wiki/CPU_cache#Associativity |
| [update] | https://en.wikipedia.org/w/index.php?title=Matrix_multiplication_algorithm&action=edit |
| [4] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-ocw-4 |
| tiled | https://en.wikipedia.org/wiki/Loop_tiling |
| [4] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-ocw-4 |
| [5] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-5 |
| [4] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-ocw-4 |
| edit | https://en.wikipedia.org/w/index.php?title=Matrix_multiplication_algorithm&action=edit§ion=3 |
| divide-and-conquer algorithm | https://en.wikipedia.org/wiki/Divide-and-conquer_algorithm |
| block partitioning | https://en.wikipedia.org/wiki/Block_matrix |
| recursively | https://en.wikipedia.org/wiki/Recursion |
| scalar multiplication | https://en.wikipedia.org/wiki/Scalar_multiplication |
| [3] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-clrs-3 |
| master theorem for divide-and-conquer recurrences | https://en.wikipedia.org/wiki/Master_theorem_(analysis_of_algorithms) |
| [3] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-clrs-3 |
| edit | https://en.wikipedia.org/w/index.php?title=Matrix_multiplication_algorithm&action=edit§ion=4 |
| [4] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-ocw-4 |
| [6] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-prokop-6 |
| unrolled | https://en.wikipedia.org/wiki/Loop_unrolling |
| edit | https://en.wikipedia.org/w/index.php?title=Matrix_multiplication_algorithm&action=edit§ion=5 |
| tiled | https://en.wikipedia.org/wiki/Loop_tiling |
| cache-oblivious | https://en.wikipedia.org/wiki/Cache-oblivious_algorithm |
| [6] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-prokop-6 |
| multiprogramming | https://en.wikipedia.org/wiki/Multiprogramming |
| [4] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-ocw-4 |
| [6] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-prokop-6 |
| edit | https://en.wikipedia.org/w/index.php?title=Matrix_multiplication_algorithm&action=edit§ion=6 |
| Computational complexity of matrix multiplication | https://en.wikipedia.org/wiki/Computational_complexity_of_matrix_multiplication |
| https://en.wikipedia.org/wiki/File:MatrixMultComplexity_svg.svg |
| Strassen's algorithm | https://en.wikipedia.org/wiki/Strassen_algorithm |
| Volker Strassen | https://en.wikipedia.org/wiki/Volker_Strassen |
| subtraction | https://en.wikipedia.org/wiki/Subtraction |
| numerical stability | https://en.wikipedia.org/wiki/Numerical_stability |
| [7] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-7 |
| [1] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-skiena-1 |
| BLAS | https://en.wikipedia.org/wiki/Basic_Linear_Algebra_Subprograms |
| [8] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-8 |
| finite fields | https://en.wikipedia.org/wiki/Finite_field |
| computer algebra systems | https://en.wikipedia.org/wiki/Computer_algebra_system |
| big-O notation | https://en.wikipedia.org/wiki/Big_O_notation |
| [9] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-9 |
| [10] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-10 |
| [11] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-11 |
| [12] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-12 |
| [13] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-13 |
| [14] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-14 |
| theoretical computer science | https://en.wikipedia.org/wiki/Theoretical_computer_science |
| asymptotic complexity | https://en.wikipedia.org/wiki/Time_complexity |
| real number | https://en.wikipedia.org/wiki/Real_number |
| Williams | https://en.wikipedia.org/wiki/Virginia_Vassilevska_Williams |
| [2] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-alman2025-2 |
| Don Coppersmith | https://en.wikipedia.org/wiki/Don_Coppersmith |
| Shmuel Winograd | https://en.wikipedia.org/wiki/Shmuel_Winograd |
| [15] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-coppersmith-15 |
| big-O notation | https://en.wikipedia.org/wiki/Big_O_notation |
| galactic algorithms | https://en.wikipedia.org/wiki/Galactic_algorithm |
| [16] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-16 |
| [17] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-robinson-17 |
| Victor Pan | https://en.wikipedia.org/wiki/Victor_Pan |
| [18] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-18 |
| Freivalds' algorithm | https://en.wikipedia.org/wiki/Freivalds'_algorithm |
| Monte Carlo algorithm | https://en.wikipedia.org/wiki/Monte_Carlo_algorithm |
| edit | https://en.wikipedia.org/w/index.php?title=Matrix_multiplication_algorithm&action=edit§ion=7 |
| DeepMind | https://en.wikipedia.org/wiki/DeepMind |
| neural network | https://en.wikipedia.org/wiki/Neural_network |
| [19] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-19 |
| clarification needed | https://en.wikipedia.org/wiki/Wikipedia:Please_clarify |
| finite field ℤ/2ℤ | https://en.wikipedia.org/wiki/GF(2) |
| [20] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-alphatensor-20 |
| remains unknown | https://en.wikipedia.org/wiki/Computational_complexity_of_matrix_multiplication#Minimizing_number_of_multiplications |
| [20] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-alphatensor-20 |
| [21] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-21 |
| [22] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-22 |
| edit | https://en.wikipedia.org/w/index.php?title=Matrix_multiplication_algorithm&action=edit§ion=8 |
| edit | https://en.wikipedia.org/w/index.php?title=Matrix_multiplication_algorithm&action=edit§ion=9 |
| divide-and-conquer algorithm | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#Divide-and-conquer_algorithm |
| parallelized | https://en.wikipedia.org/wiki/Parallel_algorithm |
| shared-memory multiprocessors | https://en.wikipedia.org/wiki/Shared-memory_multiprocessor |
| fork–join style | https://en.wikipedia.org/wiki/Fork–join_model |
| pseudocode | https://en.wikipedia.org/wiki/Pseudocode |
| [23] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-cilk-23 |
| critical path length | https://en.wikipedia.org/wiki/Critical_path_length |
| speedup | https://en.wikipedia.org/wiki/Speedup |
| [23] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-cilk-23 |
| https://en.wikipedia.org/wiki/File:Block_matrix_multiplication.svg |
| edit | https://en.wikipedia.org/w/index.php?title=Matrix_multiplication_algorithm&action=edit§ion=10 |
| distributed memory | https://en.wikipedia.org/wiki/Distributed_memory |
| Cannon's algorithm | https://en.wikipedia.org/wiki/Cannon's_algorithm |
| communication-avoiding algorithm | https://en.wikipedia.org/wiki/Communication-avoiding_algorithm |
| [24] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-24 |
| [25] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-25 |
| [26] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-irony-26 |
| [26] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-irony-26 |
| [27] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-Agarwal-27 |
| [26] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-irony-26 |
| [27] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-Agarwal-27 |
| [28] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-28 |
| MapReduce | https://en.wikipedia.org/wiki/MapReduce |
| [29] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-29 |
| edit | https://en.wikipedia.org/w/index.php?title=Matrix_multiplication_algorithm&action=edit§ion=11 |
| https://en.wikipedia.org/wiki/File:Matrix_multiplication_on_a_cross-wire_two-dimensional_array.png |
| meshes | https://en.wikipedia.org/wiki/Mesh_networking |
| Cannon's algorithm | https://en.wikipedia.org/wiki/Cannon's_algorithm |
| [30] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-30 |
| [31] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-31 |
| [32] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-32 |
| [33] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-33 |
| [34] | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_note-34 |
| edit | https://en.wikipedia.org/w/index.php?title=Matrix_multiplication_algorithm&action=edit§ion=12 |
| Computational complexity of mathematical operations | https://en.wikipedia.org/wiki/Computational_complexity_of_mathematical_operations |
| Computational complexity of matrix multiplication | https://en.wikipedia.org/wiki/Computational_complexity_of_matrix_multiplication |
| CYK algorithm § Valiant's algorithm | https://en.wikipedia.org/wiki/CYK_algorithm#Valiant's_algorithm |
| Matrix chain multiplication | https://en.wikipedia.org/wiki/Matrix_chain_multiplication |
| Method of Four Russians | https://en.wikipedia.org/wiki/Method_of_Four_Russians |
| Multiplication algorithm | https://en.wikipedia.org/wiki/Multiplication_algorithm |
| Sparse matrix–vector multiplication | https://en.wikipedia.org/wiki/Sparse_matrix–vector_multiplication |
| edit | https://en.wikipedia.org/w/index.php?title=Matrix_multiplication_algorithm&action=edit§ion=13 |
| 1 | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-skiena_1-0 |
| 2 | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-skiena_1-1 |
| 3 | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-skiena_1-2 |
| 4 | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-skiena_1-3 |
| Skiena, Steven | https://en.wikipedia.org/wiki/Steven_Skiena |
| The Algorithm Design Manual | https://archive.org/details/algorithmdesignm00skie_772 |
| 45 | https://archive.org/details/algorithmdesignm00skie_772/page/n56 |
| doi | https://en.wikipedia.org/wiki/Doi_(identifier) |
| 10.1007/978-1-84800-070-4_4 | https://doi.org/10.1007%2F978-1-84800-070-4_4 |
| ISBN | https://en.wikipedia.org/wiki/ISBN_(identifier) |
| 978-1-84800-069-8 | https://en.wikipedia.org/wiki/Special:BookSources/978-1-84800-069-8 |
| 1 | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-alman2025_2-0 |
| 2 | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-alman2025_2-1 |
| "More Asymmetry Yields Faster Matrix Multiplication" | https://epubs.siam.org/doi/10.1137/1.9781611978322.63 |
| doi | https://en.wikipedia.org/wiki/Doi_(identifier) |
| 10.1137/1.9781611978322.63 | https://doi.org/10.1137%2F1.9781611978322.63 |
| 1 | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-clrs_3-0 |
| 2 | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-clrs_3-1 |
| 3 | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-clrs_3-2 |
| Cormen, Thomas H. | https://en.wikipedia.org/wiki/Thomas_H._Cormen |
| Leiserson, Charles E. | https://en.wikipedia.org/wiki/Charles_E._Leiserson |
| Rivest, Ronald L. | https://en.wikipedia.org/wiki/Ron_Rivest |
| Stein, Clifford | https://en.wikipedia.org/wiki/Clifford_Stein |
| Introduction to Algorithms | https://en.wikipedia.org/wiki/Introduction_to_Algorithms |
| ISBN | https://en.wikipedia.org/wiki/ISBN_(identifier) |
| 0-262-03384-4 | https://en.wikipedia.org/wiki/Special:BookSources/0-262-03384-4 |
| 1 | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-ocw_4-0 |
| 2 | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-ocw_4-1 |
| 3 | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-ocw_4-2 |
| 4 | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-ocw_4-3 |
| 5 | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-ocw_4-4 |
| Leiserson, Charles | https://en.wikipedia.org/wiki/Charles_E._Leiserson |
| "6.172 Performance Engineering of Software Systems, Lecture 8" | https://web.archive.org/web/20191007160029/http://aka-ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-172-performance-engineering-of-software-systems-fall-2010/video-lectures/lecture-8-cache-efficient-algorithms/ |
| the original | http://aka-ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-172-performance-engineering-of-software-systems-fall-2010/video-lectures/lecture-8-cache-efficient-algorithms/ |
| ↑ | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-5 |
| Lam, Monica S. | https://en.wikipedia.org/wiki/Monica_S._Lam |
| doi | https://en.wikipedia.org/wiki/Doi_(identifier) |
| 10.1145/106972.106981 | https://doi.org/10.1145%2F106972.106981 |
| ISBN | https://en.wikipedia.org/wiki/ISBN_(identifier) |
| 978-0-89791-380-5 | https://en.wikipedia.org/wiki/Special:BookSources/978-0-89791-380-5 |
| 1 | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-prokop_6-0 |
| 2 | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-prokop_6-1 |
| 3 | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-prokop_6-2 |
| Prokop, Harald | https://en.wikipedia.org/wiki/Harald_Prokop |
| Cache-Oblivious Algorithms | https://web.archive.org/web/20231122003937/http://supertech.csail.mit.edu/papers/Prokop99.pdf |
| hdl | https://en.wikipedia.org/wiki/Hdl_(identifier) |
| 1721.1/80568 | https://hdl.handle.net/1721.1%2F80568 |
| the original | http://supertech.csail.mit.edu/papers/Prokop99.pdf |
| ↑ | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-7 |
| Miller, Webb | https://en.wikipedia.org/wiki/Webb_Miller |
| doi | https://en.wikipedia.org/wiki/Doi_(identifier) |
| 10.1137/0204009 | https://doi.org/10.1137%2F0204009 |
| ↑ | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-8 |
| Teukolsky, Saul A. | https://en.wikipedia.org/wiki/Saul_Teukolsky |
| Numerical Recipes: The Art of Scientific Computing | https://en.wikipedia.org/wiki/Numerical_Recipes |
| Cambridge University Press | https://en.wikipedia.org/wiki/Cambridge_University_Press |
| 108 | https://archive.org/details/numericalrecipes00pres_033/page/n131 |
| ISBN | https://en.wikipedia.org/wiki/ISBN_(identifier) |
| 978-0-521-88068-8 | https://en.wikipedia.org/wiki/Special:BookSources/978-0-521-88068-8 |
| ↑ | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-9 |
| Strassen, Volker | https://en.wikipedia.org/wiki/Volker_Strassen |
| doi | https://en.wikipedia.org/wiki/Doi_(identifier) |
| 10.1007/BF02165411 | https://doi.org/10.1007%2FBF02165411 |
| S2CID | https://en.wikipedia.org/wiki/S2CID_(identifier) |
| 121656251 | https://api.semanticscholar.org/CorpusID:121656251 |
| ↑ | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-10 |
| "On the additive complexity of matrix multiplication" | https://doi.org/10.1137%2F0205016 |
| doi | https://en.wikipedia.org/wiki/Doi_(identifier) |
| 10.1137/0205016 | https://doi.org/10.1137%2F0205016 |
| ↑ | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-11 |
| "Matrix Multiplication, a Little Faster" | https://dl.acm.org/doi/10.1145/3087556.3087579 |
| doi | https://en.wikipedia.org/wiki/Doi_(identifier) |
| 10.1145/3087556.3087579 | https://doi.org/10.1145%2F3087556.3087579 |
| ↑ | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-12 |
| doi | https://en.wikipedia.org/wiki/Doi_(identifier) |
| 10.1137/22M1502719 | https://doi.org/10.1137%2F22M1502719 |
| ↑ | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-13 |
| doi | https://en.wikipedia.org/wiki/Doi_(identifier) |
| 10.1137/0205016 | https://doi.org/10.1137%2F0205016 |
| ↑ | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-14 |
| Holtz, Olga | https://en.wikipedia.org/wiki/Olga_Holtz |
| arXiv | https://en.wikipedia.org/wiki/ArXiv_(identifier) |
| 2008.03759 | https://arxiv.org/abs/2008.03759 |
| cs.DS | https://arxiv.org/archive/cs.DS |
| ↑ | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-coppersmith_15-0 |
| Coppersmith, Don | https://en.wikipedia.org/wiki/Don_Coppersmith |
| Winograd, Shmuel | https://en.wikipedia.org/wiki/Shmuel_Winograd |
| "Matrix multiplication via arithmetic progressions" | http://www.cs.umd.edu/~gasarch/TOPICS/ramsey/matrixmult.pdf |
| doi | https://en.wikipedia.org/wiki/Doi_(identifier) |
| 10.1016/S0747-7171(08)80013-2 | https://doi.org/10.1016%2FS0747-7171%2808%2980013-2 |
| ↑ | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-16 |
| "Worst-case complexity bounds on algorithms for computing the canonical structure of finite abelian groups and the Hermite and Smith normal forms of an integer matrix" | https://web.archive.org/web/20140305182030/http://www.williamstein.org/home/wstein/www/home/pernet/Papers/Hermite/Iliopoulos88.pdf |
| doi | https://en.wikipedia.org/wiki/Doi_(identifier) |
| 10.1137/0218045 | https://doi.org/10.1137%2F0218045 |
| MR | https://en.wikipedia.org/wiki/MR_(identifier) |
| 1004789 | https://mathscinet.ams.org/mathscinet-getitem?mr=1004789 |
| the original | http://www.williamstein.org/home/wstein/www/home/pernet/Papers/Hermite/Iliopoulos88.pdf |
| ↑ | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-robinson_17-0 |
| "Toward an Optimal Algorithm for Matrix Multiplication" | https://archive.siam.org/pdf/news/174.pdf |
| ↑ | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-18 |
| doi | https://en.wikipedia.org/wiki/Doi_(identifier) |
| 10.1016/0024-3795(92)90393-O | https://doi.org/10.1016%2F0024-3795%2892%2990393-O |
| ↑ | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-19 |
| "Discovering novel algorithms with AlphaTensor" | https://www.deepmind.com/blog/discovering-novel-algorithms-with-alphatensor |
| 1 | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-alphatensor_20-0 |
| 2 | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-alphatensor_20-1 |
| "Discovering faster matrix multiplication algorithms with reinforcement learning" | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9534758 |
| Bibcode | https://en.wikipedia.org/wiki/Bibcode_(identifier) |
| 2022Natur.610...47F | https://ui.adsabs.harvard.edu/abs/2022Natur.610...47F |
| doi | https://en.wikipedia.org/wiki/Doi_(identifier) |
| 10.1038/s41586-022-05172-4 | https://doi.org/10.1038%2Fs41586-022-05172-4 |
| ISSN | https://en.wikipedia.org/wiki/ISSN_(identifier) |
| 1476-4687 | https://search.worldcat.org/issn/1476-4687 |
| PMC | https://en.wikipedia.org/wiki/PMC_(identifier) |
| 9534758 | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9534758 |
| PMID | https://en.wikipedia.org/wiki/PMID_(identifier) |
| 36198780 | https://pubmed.ncbi.nlm.nih.gov/36198780 |
| ↑ | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-21 |
| arXiv | https://en.wikipedia.org/wiki/ArXiv_(identifier) |
| 2212.01175 | https://arxiv.org/abs/2212.01175 |
| cs.SC | https://arxiv.org/archive/cs.SC |
| ↑ | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-22 |
| "AI Reveals New Possibilities in Matrix Multiplication" | https://www.quantamagazine.org/ai-reveals-new-possibilities-in-matrix-multiplication-20221123/ |
| 1 | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-cilk_23-0 |
| 2 | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-cilk_23-1 |
| Cilk: Efficient Multithreaded Computing | https://web.archive.org/web/20201106232735/http://supertech.csail.mit.edu/papers/randall-phdthesis.pdf |
| hdl | https://en.wikipedia.org/wiki/Hdl_(identifier) |
| 1721.1/47519 | https://hdl.handle.net/1721.1%2F47519 |
| the original | http://supertech.csail.mit.edu/papers/randall-phdthesis.pdf |
| ↑ | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-24 |
| A cellular computer to implement the Kalman Filter Algorithm | https://dl.acm.org/doi/abs/10.5555/905686 |
| ↑ | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-25 |
| Kung, H. T. | https://en.wikipedia.org/wiki/H._T._Kung |
| "I/O complexity: The red-blue pebble game" | https://apps.dtic.mil/dtic/tr/fulltext/u2/a104739.pdf |
| doi | https://en.wikipedia.org/wiki/Doi_(identifier) |
| 10.1145/800076.802486 | https://doi.org/10.1145%2F800076.802486 |
| S2CID | https://en.wikipedia.org/wiki/S2CID_(identifier) |
| 8410593 | https://api.semanticscholar.org/CorpusID:8410593 |
| Archived | https://web.archive.org/web/20191215182754/https://apps.dtic.mil/dtic/tr/fulltext/u2/a104739.pdf |
| 1 | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-irony_26-0 |
| 2 | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-irony_26-1 |
| 3 | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-irony_26-2 |
| doi | https://en.wikipedia.org/wiki/Doi_(identifier) |
| 10.1016/j.jpdc.2004.03.021 | https://doi.org/10.1016%2Fj.jpdc.2004.03.021 |
| 1 | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-Agarwal_27-0 |
| 2 | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-Agarwal_27-1 |
| doi | https://en.wikipedia.org/wiki/Doi_(identifier) |
| 10.1147/rd.395.0575 | https://doi.org/10.1147%2Frd.395.0575 |
| ↑ | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-28 |
| Demmel, James | https://en.wikipedia.org/wiki/James_Demmel |
| "Communication-optimal parallel 2.5D matrix multiplication and LU factorization algorithms" | https://solomonik.cs.illinois.edu/talks/europar-sep-2011.pdf |
| doi | https://en.wikipedia.org/wiki/Doi_(identifier) |
| 10.1007/978-3-642-23397-5_10 | https://doi.org/10.1007%2F978-3-642-23397-5_10 |
| ISBN | https://en.wikipedia.org/wiki/ISBN_(identifier) |
| 978-3-642-23397-5 | https://en.wikipedia.org/wiki/Special:BookSources/978-3-642-23397-5 |
| ↑ | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-29 |
| "Dimension Independent Matrix Square Using MapReduce" | https://stanford.edu/~rezab/papers/dimsum.pdf |
| arXiv | https://en.wikipedia.org/wiki/ArXiv_(identifier) |
| 1304.1467 | https://arxiv.org/abs/1304.1467 |
| Bibcode | https://en.wikipedia.org/wiki/Bibcode_(identifier) |
| 2013arXiv1304.1467B | https://ui.adsabs.harvard.edu/abs/2013arXiv1304.1467B |
| ↑ | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-30 |
| "A faster parallel algorithm for matrix multiplication on a mesh array" | https://www.sciencedirect.com/science/article/pii/S1877050914003858/pdf |
| doi | https://en.wikipedia.org/wiki/Doi_(identifier) |
| 10.1016/j.procs.2014.05.208 | https://doi.org/10.1016%2Fj.procs.2014.05.208 |
| ↑ | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-31 |
| doi | https://en.wikipedia.org/wiki/Doi_(identifier) |
| 10.1016/0167-8191(88)90078-6 | https://doi.org/10.1016%2F0167-8191%2888%2990078-6 |
| ↑ | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-32 |
| arXiv | https://en.wikipedia.org/wiki/ArXiv_(identifier) |
| 1411.3273 | https://arxiv.org/abs/1411.3273 |
| cs.DC | https://arxiv.org/archive/cs.DC |
| ↑ | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-33 |
| doi | https://en.wikipedia.org/wiki/Doi_(identifier) |
| 10.1016/0020-0255(88)90010-2 | https://doi.org/10.1016%2F0020-0255%2888%2990010-2 |
| ↑ | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#cite_ref-34 |
| doi | https://en.wikipedia.org/wiki/Doi_(identifier) |
| 10.1137/0210049 | https://doi.org/10.1137%2F0210049 |
| edit | https://en.wikipedia.org/w/index.php?title=Matrix_multiplication_algorithm&action=edit§ion=14 |
| Dongarra, Jack | https://en.wikipedia.org/wiki/Jack_Dongarra |
| arXiv | https://en.wikipedia.org/wiki/ArXiv_(identifier) |
| 0709.1272 | https://arxiv.org/abs/0709.1272 |
| doi | https://en.wikipedia.org/wiki/Doi_(identifier) |
| 10.1016/j.parco.2008.10.002 | https://doi.org/10.1016%2Fj.parco.2008.10.002 |
| S2CID | https://en.wikipedia.org/wiki/S2CID_(identifier) |
| 955 | https://api.semanticscholar.org/CorpusID:955 |
| doi | https://en.wikipedia.org/wiki/Doi_(identifier) |
| 10.1145/1356052.1356053 | https://doi.org/10.1145%2F1356052.1356053 |
| S2CID | https://en.wikipedia.org/wiki/S2CID_(identifier) |
| 9359223 | https://api.semanticscholar.org/CorpusID:9359223 |
| doi | https://en.wikipedia.org/wiki/Doi_(identifier) |
| 10.1145/2764454 | https://doi.org/10.1145%2F2764454 |
| S2CID | https://en.wikipedia.org/wiki/S2CID_(identifier) |
| 1242360 | https://api.semanticscholar.org/CorpusID:1242360 |
| How To Optimize GEMM | https://github.com/flame/how-to-optimize-gemm |
| v | https://en.wikipedia.org/wiki/Template:Numerical_linear_algebra |
| t | https://en.wikipedia.org/wiki/Template_talk:Numerical_linear_algebra |
| e | https://en.wikipedia.org/wiki/Special:EditPage/Template:Numerical_linear_algebra |
| Numerical linear algebra | https://en.wikipedia.org/wiki/Numerical_linear_algebra |
| Floating point | https://en.wikipedia.org/wiki/Floating_point |
| Numerical stability | https://en.wikipedia.org/wiki/Numerical_stability |
| System of linear equations | https://en.wikipedia.org/wiki/System_of_linear_equations |
| Matrix decompositions | https://en.wikipedia.org/wiki/Matrix_decomposition |
| Matrix multiplication | https://en.wikipedia.org/wiki/Matrix_multiplication |
| algorithms | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm |
| Matrix splitting | https://en.wikipedia.org/wiki/Matrix_splitting |
| Sparse problems | https://en.wikipedia.org/wiki/Sparse_matrix |
| CPU cache | https://en.wikipedia.org/wiki/CPU_cache |
| TLB | https://en.wikipedia.org/wiki/Translation_lookaside_buffer |
| Cache-oblivious algorithm | https://en.wikipedia.org/wiki/Cache-oblivious_algorithm |
| SIMD | https://en.wikipedia.org/wiki/Single_instruction,_multiple_data |
| Multiprocessing | https://en.wikipedia.org/wiki/Multiprocessing |
| ATLAS | https://en.wikipedia.org/wiki/Automatically_Tuned_Linear_Algebra_Software |
| MATLAB | https://en.wikipedia.org/wiki/MATLAB |
| Basic Linear Algebra Subprograms (BLAS) | https://en.wikipedia.org/wiki/Basic_Linear_Algebra_Subprograms |
| LAPACK | https://en.wikipedia.org/wiki/LAPACK |
| Specialized libraries | https://en.wikipedia.org/wiki/Comparison_of_linear_algebra_libraries |
| https://en.wikipedia.org/w/index.php?title=Matrix_multiplication_algorithm&oldid=1380115136 | https://en.wikipedia.org/w/index.php?title=Matrix_multiplication_algorithm&oldid=1380115136 |
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